A parabola with focus F(4, 5) and directrix y = -13 contains the point P(x, y).
y=-13
F(4,5)
P(x,y)
PD=
D(x,-13)
13
First, we will find an expression for the distance from P, a random point on the
parabola, to the directrix.
Write an expression for PD and simplify if necessary:

Using conditional probability, it is found that the correct statement is given by:

C. If P(A | B) = P(A) and P(B | A) = P(B), then the events are independent.

Conditional probability is the probability of one event happening, considering a previous event. The formula is:

\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)

In which:

If two events are independent, we have that:

\(P(A \cap B) = P(A)P(B)\).

Hence:

\(P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{P(A)P(B)}{P(A)} = P(B)\)

\(P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{P(A)P(B)}{P(B)} = P(A)\)

Which means that option C is correct.

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The number of mosquitoes will be increased by 5 inches of rain.

Maximum mosquito population = 25000

We are given the following in the question:

M(x) = 10x - x²

where M(x) denotes the number of mosquitos in millions and x denotes the amount of rainfall in inches.

To begin, we differentiate M(x) with respect to x, yielding

d(M(x)) /dx = d(10x - x²) /dx = 10 -2x

When we set the first derivative to zero, we get

d(M(x)) /dx = 0

10 - 2x = 0

x = 5

We get the same result when we differentiate M(x) with respect to x:

d²(M(x)) / dx² = -2

d²(M(x)) / dx² < 0

As a result of the double differentiation test, the maxima for M(x) occur at x = 5.

when the rainfall is 5 inches, the most mosquitoes are present.

Maximum mosquito population:

M(5) = 10(5) - (5)² = 25

As a result, the maximum number of mosquitos is 25000.

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The disadvantages of the mode are: For many sets of data there is no mode.

The mode is a measure of central tendency that represents the most frequently occurring value in a dataset.

However, one of the disadvantages of the mode is that for many sets of data, there may not be a distinct mode. In such cases, the data may have a uniform distribution where all values occur with equal frequency, or it may have multiple modes with similar frequencies.

The mode is not affected by extremely large or small values. It only considers the frequency of values and not their magnitude. Therefore, extreme values do not influence the mode.

The statement that the mode can only be computed for interval-level data or higher is incorrect. The mode can be computed for any type of data, including nominal, ordinal, interval, and ratio data. It is applicable to categorical as well as numerical data.

The main disadvantage of the mode is that for many datasets, there may not be a distinct mode.

The correct option is: For many sets of data there is no mode.

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The sum accumulated by 31st December 2018 is Rs 4,163,060.00

What is future value?

Future value is the accumulated amount that investments would yield in future period when the amounts invested are added with the total interest earned.

Note in this case that Rs500,000  would be invested subsequently for 4 years( 2015-2018 , January 1st of each year)

We can determine the future value of each investment using the future value formula shown below:

FV=PV*(1+r)^N

PV=amount invested

r=interest=10%

N=number of years that an amount is invested(for instance, the amount invested on 1st January 2014 will earn interest in 2014,2015,2016, 2017 and 2018 i.e. for 4 years)

Total FV=1,000,000*(1+10%)^5+500,000*(1+10%)^4+500,000*(1+10%)^3+500,000*(1+10%)^2+500,000*(1+10%)^1

Total FV=Rs 4,163,060.00

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Answer:

3.14

That is the value of pi to the second decimal point

The equation of the line in slope-point form is:

y - 7 = -4/5(x + 6)

The equation of a line in slope-point form is given by:

y - y₁ = m(x - x₁)

where:

(x₁, y₁) represents the coordinates of a point on the line.

m represents the slope of the line.

m = (y₂ - y₁)/(x₂ - x₁)

(x₁, y₁) represents the coordinates of the 1st point on the line

where (x₂, y₂) represents the coordinates of the 2nd point on the line

We have

(x₁, y₁) = (-6, 7)

(x₂, y₂) = (4, -1)

m = (y₂ - y₁)/(x₂ - x₁)

m = (-1 - 7) / (4 - (-6))

m = -8/10

m = -4/5

Using y - y₁ = m(x - x₁):

y - 7 = -4/5(x - (-6))

y - 7 = -4/5(x + 6)

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This is a problem finding the slope of a line at some point "a"

It accomplishes this by doing an average rate of change formula over an area approaching 0.

We must know the format of this type of equation.

See first image.

The variables in this example don't match up.

Let the function input be x, and the limit being a --> 0

a = 2

f(x) = x^5

Answer:

\(\displaystyle{f(x)=x^4 \ \: \text{and} \ \: a =2}\)

Step-by-step explanation:

The first principal of derivative:

\(\displaystyle{f'(x) = \lim_{h\to 0} \dfrac{f(x+h)-f(x)}{h}}\)

Since the given problem represents f'(a), meaning:

\(\displaystyle{f'(a) = \lim_{h\to 0} \dfrac{f(a+h)-f(a)}{h}}\)

If we compare:

\(\displaystyle{f'(a) = \lim_{h\to 0} \dfrac{f(a+h)-f(a)}{h}}\)

and

\(\displaystyle{ \lim_{h\to 0} \dfrac{(2+h)^4-16}{h}}\)

which can be rewriten as:
\(\displaystyle{f'(a) = \lim_{h\to 0} \dfrac{(2+h)^4-2^4}{h}}\)

We can conclude by comparing that:

This would mean that:

\(\displaystyle{f(x)=x^4}\)

Therefore:

\(\displaystyle{f(x)=x^4 \ \: \text{and} \ \: a =2}\)

Answer: x = -1

Step-by-step explanation:

simplify 2(x + 7) 2 / 3 = 8 to 4x + 28 = 24 and then solve it from there

When the former image is rotated, the dots will be located at section 2 and 7.

When an image is rotated, the constituents within it also changes its position as the object is moves from a point to another about a pivot junction.

From the given image above, after the rotation of the initial image, the dot should be located at number 2 and 7 of the new image.

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Domain: All real numbers (-infinity, infinity)

Range: [9, -infinity)

Applying the area of a square, the total area of the design is: 116 cm²

A square has equal side lengths, s, this, the area of a square is given as: A = s².

The three pieces of square shaped cloth that Jordan made the design from is shown in the image attached below.

To find the total area of the design, find the area of each square shaped cloth and add all together.

Thus, applying the area of a square, the total area would be:

Total Area = 4² + 6² + 8²

Total Area = 116 cm²

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\(x ^{3} - 3x - 2 \)

x³-2x²+2x²-3x-2

x²(x-2)+2x²-4x+1x-2

x²(x-2)+2x(x-2)+1(x-2)

(x-2)(x²+2x+1)

(x-2)(x+1)(x+1)is a required answer.

Using the Central Limit Theorem, it is found that:

a) The shape is approximately normal.

b) It targets the population mean.

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the sampling distribution is also approximately normal, as long as n is at least 30.

Item a:

The variable is skewed, however, the sample size is greater than 30, hence the approximate shape of the distribution is normal.

Item b:

According to the mean of the sampling distributions, given by the Central Limit Theorem, it targets the population mean.

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Answer:

Step-by-step explanation:

Hi

Answer:

13.24

Step-by-step explanation:

Your buying a shirt not shorts

Answer:6 hours have passed by.

Step-by-step explanation:

0.8x= 84-79.2 where x is the number of hours.

O.8x = 4.8

Divide both sides by 0.8

X= 6

Answer:

81^84375

Step-by-step explanation:

Answer: ( -\(\sqrt{5}\) / 3)

Step-by-step explanation:

sin(angle) = opposite/hypotenuse

opposite =2

hypotenuse = 3

solve for adjacent side with pythagorean theorum

opposite^2 + adjacent^2 = hypotenuse^2

2^2 + adjacent^2 = 3^2

4 + adjacent^2 = 9

adjacent^2 = 9 - 4

adjacent^2 = 5

adjacent = \(\sqrt{5}\)

-\(\sqrt{5}\) since it is in the second quadrant

cosx = (adjacent/hypotenuse)

cosx = (-\(\sqrt{5}\)/3)

(-\(\sqrt{5}\)/3)

The step in which the subtraction property of equality was applied to solve the equation is given as follows:

D. The subtraction property of equality was not applied to solve this equation.

The subtraction property of equality states that subtracting the same number from both sides of an equation does not affect the equality, and hence it is used to isolate a variable that is adding on a side of the expression.

For this problem, to remove the term -7, we add 7 to both sides of the expression, hence the addition property of equality was applied.

In the other step, the multiplication property was applied, hence option D is the correct option for this problem.

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The interval which contains the median water bill is $200 - $225

The tabulated data :

Class interval ____ Frequency ___ Cummulative frequency

100 to 125, ________ 1 ___________ 1

125 to 150, 2 ______ 2 ___________3

150 to 175, 5 _______5 ___________8

175 to 200, 10 ______10 __________18

200 to 225, 13 _____13 __________ 31

225 to 250, _______ 8 __________40

The median class = Cummulative frequency / 2

The median class = 40 / 2

The class interval which contains the 20th frequency.

This is the 200 - 225 class

The interval which contains the median water bill is $200 - $225

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The scenario that will bring about a type II error will be when the true mean is 405 ppm and he uses a significance level of 0.15

It should be noted that a type II error simply describes the error that occurs when the individual fails to reject a null hypothesis.

From the complete question, type II error will be when the true mean is 405 ppm and he uses a significance level of 0.15. In this case, the null hyothesis was not rejected.

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Answer:

Step-by-step explanation:

Answer:

Amadi: 20 years old

Chima : 4 years old

The simplified ratio of total marbles to red marbles is 27 to 8

In this question, we have the following parameters

Blue marbles = 24

Red marbles = 16

White marbles = 14

The above parameters mean that

Total marbles = sum of the individual marbles

Substitute the known values in the above equation, so, we have the following representation

Total marbles = 24 + 16 + 14

Evaluate

Total marbles = 54

The ratio is then represented as

Ratio = Total : Red

This gives

Ratio = 54 : 16

Simplify ratio

Ratio = 27 : 8

Hence, the simplified ratio is 27 : 8

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Answer:

A. 10x=350

B. 35 inches

Step-by-step explanation:

So the first piece is x, and the second is 3 times as long, so the second is 3x, and the third pice is twice as long has the second piece which is 3x, so third piece is 6x. The total is 350 inches, so x+3x+6x=350. Simplify that so you get 10x=350. Divide both sides by 10, and you get x=35 inches. Hope that helps!

Answer:

the answer is 0.428

Step-by-step explanation:

i did the math

The amount that I spent by using the equation y = 1/2x , according to my friend's expense is $7.5.

In its simplest form in algebra, the definition of an equation is a mathematical statement that two mathematical expressions are equal. For example, 3x + 5 = 14 is an equation where 3x + 5 and 14 are two terms separated by an equal sign. 

There are two types of equations:

Identities and conditionals. The identity applies to all values ​​of the variable. Constraint expressions apply only to specific values ​​of variables. Equations are written as two expressions separated by an equal sign ("="). 

Solution:

Given, amount spent by friend = $15

           Equation: y = 1/2x

So, amount spent by me is as follows

y = (1/2)×15

  =15/2

y  = $7.5

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The amount of money you are spending is $7.50 according to the given equation.

A mathematical equation is a statement that expresses the relationship between two values using mathematical symbols. An equation typically involves a variable, which is a symbol that stands for a number that can change, and an equals sign. Equations can be used to solve a variety of problems in mathematics.

The equation y = 1/2x states that 'y' is equal to one half of 'x'. This equation can be used in many different ways to solve real-life problems. In this case, 'x' represents the amount of money your friend spent at the carnival. 'y' represents the amount of money you spent. To solve for 'y', we divide the value of 'x' by 2.

In the question, your friend spent $15 at the carnival. Therefore, 'x' is equal to 15. We then divide 15 by 2, which gives us 7.5. This means that you spent $7.50 at the carnival.

The equation y = 1/2x is a simple but powerful tool for solving problems. It can be used for a variety of tasks, including finding out how much money you spent at the carnival if you spent half as much as your friend. All you have to do is plug in the value of 'x' and divide it by two.

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9514 1404 393

Answer:

  30x +25y = 148

Step-by-step explanation:

We can use substitution to find the point of intersection of ...

Using the second equation, we can write an expression for y:

  y = 6 -x

Substituting that into the first equation gives ...

  3x +14 = 2(6 -x)

  3x +14 = 12 -2x . . . . . eliminate parentheses

  5x = -2 . . . . . . . . . . . add 2x-14

  x = -0.4 . . . . . . . . . divide by 5

  y = 6 -(-0.4) = 6.4

__

Now, we want an equation for a line through the point (-0.4, 6.4) that is perpendicular to 5x = 6y+1

The perpendicular line will have the coefficients swapped with one of them negated. The constant will accommodate the given point.

  6x = -5y + c

  6(-0.4) +5(6.4) = c = 29.6

The perpendicular line can be written ...

  6x = -5y +29.6

In standard form, the equation is ...

  30x +25y = 148

Answer:

4.8

Step-by-step explanation:

\( V_{sphere} = \frac{4}{3} \pi r^3 \)

\( 144\pi= \frac{4}{3} \pi r^3 \)

\(r^3 = \frac {3 \times 144\pi}{4\pi}\)

\(r^3 = 3 \times 36\)

\(r^3 = 108\)

\(r = \sqrt[3]{108} \\ \\ r = 4.7622031559 \\ \\ r \approx \: 4.8 \: \)